Following the proof of Lemma 3.3.1 in [1]}, one can show that \(\mathbf {G}\)  is a nonempty Zariski open subset of \(\mathbf {M}_{(0,2\theta ,-4)}\) . Following the proof of Corollary 3.3.3 in [1]}, one can show the open subset \(\mathbf {G}^B \subset \mathbf {M}_{(0,2\theta ,-4)}^B\)  can be identified with the relative degree-0 Picard scheme \(\textup {Pic}^0_{\mathcal {C}/B}\)  of the family \(\mathcal {C}/B\)  of curves in the linear system \(B\) . Using this identification, the morphism \(\mathbf {M}_{(0,2\theta ,-4)} \xrightarrow{} J^\vee \times J \xrightarrow{} J\)  restricted to \(\mathbf {G}^B\)  induces a morphism \(\mathbf {a}\colon \textup {Pic}^0_{\mathcal {C}/B} \rightarrow J \times B\)  which fiberwise is the map
\(a \colon \textup {Pic}^0(C_b) \rightarrow J; \quad L \mapsto \sum c_2(i_{b*}L).\) 
